There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We present a review of experimental and theoretical studies of the anomalous Hall effect (AHE), focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical work, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents which originate from spin-orbit coupling. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors, have more clearly established systematic trends. These two developments in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of Berry-phase curvatures and it is therefore an intrinsic quantum mechanical property of a perfect cyrstal. An extrinsic mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. We review the full modern semiclassical treatment of the AHE together with the more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Finally we discuss outstanding issues and avenues for future investigation.

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Anomalous hall effect

Using the full-potential screened Korringa-Kohn-Rostoker method we study the full-Heusler alloys based on Co, Fe, Rh, and Ru. We show that many of these compounds show a half-metallic behavior; however, in contrast to the half-Heusler alloys the energy gap in the minority band is extremely small due to states localized only at the Co (Fe, Rh, or Ru) sites which are not present in the half-Heusler compounds. The full-Heusler alloys show a Slater-Pauling behavior and the total spin magnetic moment per unit cell ${(M}_{t})$ scales with the total number of valence electrons ${(Z}_{t})$ following the rule ${M}_{t}{=Z}_{t}\ensuremath{-}24.$ We explain why the spin-down band contains exactly 12 electrons using arguments based on group theory and show that this rule holds also for compounds with less than 24 valence electrons. Finally we discuss the deviations from this rule and the differences compared to the half-Heusler alloys.

/pdf/slater-pauling-behavior-and-origin-of-the-half-metallicity-1vlzvqk1h0.pdf

Slater-Pauling behavior and origin of the half-metallicity of the full-Heusler alloys

Simple rules for the understanding of Heusler compounds

Spintronics is a multidisciplinary field involving physics, chemistry, and engineering, and is a new research area for solid-state scientists. A variety of new materials must be found to satisfy different demands. The search for ferromagnetic semiconductors and stable half-metallic ferromagnets with Curie temperatures higher than room temperature remains a priority for solid-state chemistry. A general understanding of structure-property relationships is a necessary prerequisite for the design of new materials. In this Review, the most important developments in the field of spintronics are described from the point of view of materials science.

Spintronics: a challenge for materials science and solid-state chemistry.

We study the origin of the gap and the role of chemical composition in the half-ferromagnetic Heusler alloys using the full-potential screened Korringa-Kohn-Rostoker method. In the paramagnetic phase the ${C1}_{b}$ compounds, like NiMnSb, present a gap. Systems with 18 valence electrons, ${Z}_{t},$ per unit cell, like CoTiSb, are semiconductors, but when ${Z}_{t}g18,$ antibonding states are also populated, thus the paramagnetic phase becomes unstable and the half-ferromagnetic one is stabilized. The minority occupied bands accommodate a total of nine electrons and the total magnetic moment per unit cell in ${\ensuremath{\mu}}_{B}$ is just the difference between ${Z}_{t}$ and $2\ifmmode\times\else\texttimes\fi{}9.$ While the substitution of the transition metal atoms may preserve the half-ferromagnetic character, substituting the sp atom results in a practically rigid shift of the bands and the loss of half-metallicity. Finally we show that expanding or contracting the lattice parameter by 2% preserves the minority-spin gap.

/pdf/origin-and-properties-of-the-gap-in-the-half-ferromagnetic-1d93np84qf.pdf

Origin and properties of the gap in the half-ferromagnetic Heusler alloys

Intermetallic Heusler alloys are amongst the most attractive half-metallic systems due to their high Curie temperatures and their structural similarity to binary semiconductors. In this review we present an overview of the basic electronic and magnetic properties of both Heusler families: the so-called half-Heusler alloys like NiMnSb and the full-Heusler alloys like Co2MnGe. Ab initio results suggest that both the electronic and magnetic properties in these compounds are intrinsically related to the appearance of the minority-spin gap. The total spin magnetic moment Mt scales linearly with the number of the valence electrons Zt, such that Mt = Zt − 24 for the full-Heusler and Mt = Zt − 18 for the half-Heusler alloys, thus opening the way to engineer new half-metallic alloys with the desired magnetic properties.

https://iopscience.iop.org/article/10.1088/0022-3727/39/5/S01/pdf

Electronic structure and Slater–Pauling behaviour in half-metallic Heusler alloys calculated from first principles

Intermetallic Heusler alloys are amongst the most attractive half-metallic systems due to the high Curie temperatures and the structural similarity to the binary semiconductors. In this review we present an overview of the basic electronic and magnetic properties of both Heusler families: the so-called half-Heusler alloys like NiMnSb and the the full-Heusler alloys like Co2MnGe. Ab-initio results suggest that both the electronic and magnetic properties in these compounds are intrinsically related to the appearance of the minority-spin gap. The total spin magnetic moment Mt scales linearly with the number of the valence electrons Zt, such that Mt = Zt − 24 for the full-Heusler and Mt = Zt − 18 for the half-Heusler alloys, thus opening the way to engineer new half-metallic alloys with the desired magnetic properties.

Introduction to half-metallic Heusler alloys: Electronic Structure and Magnetic Properties

We report systematic first-principles calculations for ordered zinc-blende compounds of the transition metal elements V, Cr, and Mn with the $\mathrm{sp}$ elements N, P, As, Sb, S, Se, and Te, motivated by a recent fabrication of zinc-blende CrAs, CrSb, and MnAs. They show a ferromagnetic half-metallic behavior for a wide range of lattice constants. We discuss the origin and trends of half-metallicity, present the calculated equilibrium lattice constants, and examine the half-metallic behavior of their transition element terminated (001) surfaces.

/pdf/zinc-blende-compounds-of-transition-elements-with-n-p-as-sb-2kw0ndaffu.pdf

Iosif Galanakis

Papers

Slater-Pauling behavior and origin of the half-metallicity of the full-Heusler alloys

Origin and properties of the gap in the half-ferromagnetic Heusler alloys

Electronic structure and Slater–Pauling behaviour in half-metallic Heusler alloys calculated from first principles

Introduction to half-metallic Heusler alloys: Electronic Structure and Magnetic Properties

Zinc-blende compounds of transition elements with N, P, As, Sb, S, Se, and Te as half-metallic systems